Predicting the rise in bread: is it that easy?

Monika Bartyzel on Slashfood did an interesting article recently on altering the amount of yeast that you use for cold-fermenting bread. The idea behind cold-fermentation is that that you keep the dough cold so that the yeast aren't particularly active. This allows the various enzymatic activities with the dough to happen on their own over time, increasing the flavor of the bread. That works especially well with non-enriched breads. There was a post that Monkia refers to that discusses a specific recipe someone is developing for a cinnamon bread that slow rises. In the comments of that post, someone suggests the baker's formula:
Original Amount of Yeast * Original Fermentation Time
New Fermentation Time
Now, the commenter didn't say explicitly that this formula was for cold-fermenting breads. Also, I have to say that I'm a little suspicious of the simplicity of the formula. It could be that everything just works out fine with it, because there are a lot of close-enoughs that make it work out. But yeast don't reproduce in a linear fashion, they reproduce exponentially. Under ideal conditions, yeast will double in size every generation. So instead of starting with 2 yeast, then having 4 the next generation, the 6 the next, then 8, 10, 12, and 14, we start with 2, then 4,8,16,32,64,128,256. After a while, the yeast by-products, alcohol in particular, will kill off the yeast, so they can only go so far before they all die off. However, given their exponential growth beforehand, you can see that the amount of time that passes should eventually have a much greater effect on yeast reproduction than the amount that you reduce the initial batch by. So if I started with 30 yeasts instead of 60 yeasts, according to the formula I would be able to double the amount of time that it takes the bread to rise. But let's assume our target is 6000 yeasts, With the 30 yeasts it would take: 30, 60, 120, 240, 480, 960, 1920, 3840, and over 6000 the next generation, or about 9 generations. With the 60 yeasts, it would take: 60, 120, 240, 480, 960, 1920, 3840, and over 6000 the next generation, or about 8 generations. That's not a huge time difference, and it gets smaller the longer you let it go (to a point). Of course, there are other factors. There's the amount of food available (the sugars and the potential sugars), the temperature of the environment, and if there are any wild yeasts ready to jump on the bandwagon. With the cold-storage method, you control the temperature and the ability for wild yeasts to interfere, so that may help settle things down into what is, for all intents and purposes, a linear scale. So, while I'm not saying that the formula is wrong, I am saying that it looks suspicious. A little too easy. Quiet… too quiet. I've got a bad feeling about this. I do not think it means what you think it means. It's probably a good starting point, but I will do some experimentation in my own kitchen before I decide that I can put this dough in my fridge for almost exactly 16 hours and be ready to have perfect bread in time for my dinner party that night.

Fractal Foods

Fractals are constructs that, when you look closely at them, contain tiny copies of themselves. There are fractals all over nature, and there was a period in the early nineties, around the time of the first Jurassic Park, that fractals and chaos theory were intensely popular. The most popular mathematical fractal, the Mandelbrot set, was featured on t-shirts and posters everywhere, and how quickly your computer could generate one was the Big Nerd equivalent of how quickly your car could go from 0 to 60 MPH.* Note that the audio to the video contains not only a naughty word or two, but extreme geekery in the form of a Jonathan Coulton song. In the world of living creatures, fractals aren't quite as popular. If you met a bear that was a fractal bear, he'd probably look like this:
and that'd just be weird, right? Vegetables are a little different though; at least a few of them are. People talk about onions having layers like that's something interesting, but the broccoli relatives are the ones that you want to watch out for. If you've ever cut up a broccoli or cauliflower, you've probably noticed that the little stalks are much like the larger bits, at least up until a point. The best representation of a fractal that I've seen in nature is broccoli's cousin, the romanesco. The first time you see one, you tend to think "pointy broccoli." That's because it looks like:
Image courtesy of PD under a Creative Commons Public Domain license. which, as you can clearly see, is a pointy broccoli, or something that looks suspiciously like a pointy broccoli. *- The "Magic Eye" or random dot 3D autostereograms were also very popular at that time.** **- Ooh, and fiber optic artwork. People loved that stuff.